A 2019 demonstration by Gao et al. (imec) showed that a polymer-based piezoelectric micromachined ultrasonic transducer (PMUT) array can perform multi-frequency pulse-echo ultrasound imaging: several flexural membrane modes of a single aperture are excited so that one array images at a low-frequency band for deep penetration and at higher-frequency bands for fine resolution. The demonstration left central questions open: why resonances measured on single devices (such as the roughly 4 MHz third flexural mode, M03, of the 320 µm devices) are suppressed or altered when the devices operate as an array; what noise floor and end-to-end signal-to-noise ratio (SNR), including front-end electronics, such arrays achieve; how penetration depth scales with drive frequency; and what design rules follow from the frequency-dependent trade-offs among transmit pressure, receive sensitivity, and resolution. Follow-up work has established fluid-borne acoustic crosstalk as a general origin of array-level modes, and multi-frequency PMUT imaging has been demonstrated on other piezoelectric platforms, but no published work provides a validated predictive account of which single-device resonances survive array operation, a systematic end-to-end SNR and penetration-depth-versus-frequency characterization, or quantified multi-frequency design rules.

Background

A piezoelectric micromachined ultrasonic transducer (PMUT) is a micro-electromechanical (MEMS) device in which a thin circular membrane carrying a piezoelectric film vibrates in flexural modes to transmit and receive ultrasound; unlike bulk piezoelectric transducers, PMUTs can be fabricated in dense arrays over large and even flexible substrates, which makes them attractive for portable and wearable ultrasound imaging. In the polymer implementation of Gao et al. (2019), each membrane is a roughly 15 µm polyimide layer (a flexible polymer) with a 500 nm PVDF film (polyvinylidene fluoride, a flexible polymer piezoelectric), protected by a parylene coating (parylene being a conformal protective polymer film deposited from vapor). Conventional pulse-echo imaging — in which the same transducer emits a pulse and records the echoes reflected by acoustic impedance contrasts — is governed by a single resolution-penetration trade-off: higher ultrasound frequency yields finer axial resolution (along the beam) and lateral resolution (across the beam) but is attenuated more strongly in tissue, so it reaches shallower depths. A multi-frequency array aims to escape this trade-off by driving several flexural membrane modes (M01, M02, M03, ... — the fundamental and successively higher-order axisymmetric vibration modes of the circular membrane, each with its own resonance frequency and nodal-ring pattern) of one and the same aperture, so a single array can image at a low-frequency band for penetration and at higher-frequency bands for resolution.

Gao et al. (2019) characterized this concept for polymer PMUTs: single-device resonance frequencies and mode shapes measured in air and in water agreed with finite-element simulations that included membrane pre-stress and fluid loading (for a 320 µm device, immersion shifts the first four modes from about 0.7, 2.7, 5.2 and 7.6 MHz in air to about 0.3, 1.7, 4.0 and 6.8 MHz in water); a donut-shaped top electrode was optimized to drive the second mode (M02) efficiently; a 5×5 array of 320 µm devices driven across 1.7–20 MHz produced measurable on-axis pressure at roughly 2, 8 and 15 MHz, but the expected pressure peak near 4 MHz — the single-device M03 resonance in water — did not appear; a large two-dimensional array of 400 µm devices produced a pressure map consistent with k-Wave acoustic simulation (k-Wave being an open-source acoustic propagation simulator), a receive sensitivity of 19 mV/MPa measured only at 1.1 MHz, and pulse-echo echoes from a plate phantom at 38 mm and 63 mm depth. The paper reported no noise floor, no SNR analysis, and no penetration-depth-versus-frequency mapping.

When many resonant membranes operate together, each element no longer behaves as an isolated resonator: neighboring membranes couple through the surrounding fluid (mutual acoustic loading — the pressure radiated by one membrane loads the others, shifting and hybridizing resonances into collective array modes), through the shared substrate, and through the electrical addressing network used to drive and read out the array (for two-dimensional arrays, row-column addressing — addressing elements by row and column lines rather than individual leads, as demonstrated for PMUTs by Liu et al. 2022 and Joshi et al. 2024 — is one common scheme). Array-level crosstalk in PMUT arrays had been modeled before this work (Wang and Horsley 2017, a mutual acoustic impedance model; Pirouz et al. 2019, finite-element analysis of a 64-element array of 80 membranes each), but the 2019 polymer-array results posed the question concretely for multi-frequency imaging: which single-device resonances survive array operation, why, and with what consequences for the SNR, penetration depth, and resolution achievable in each frequency band.

Problem Statement

For polymer-based multi-frequency PMUT arrays of the type demonstrated by Gao et al. (2019), establish the array-level performance physics needed to make single-aperture multi-frequency pulse-echo imaging quantitatively predictable and designable. Three linked components serve this one objective: (1) Resonance modification: identify which of the following candidate mechanisms dominate in suppressing or altering single-device resonances when the devices operate as an array — fluid-borne mutual acoustic loading, substrate/structural coupling, electrical addressing and crosstalk, and superposition of the radiated fields — and experimentally validate the dominant mechanism or mechanisms, to the point of predicting, for a given membrane geometry, pitch, electrode coverage and addressing scheme, which single-device modal resonances appear in the array transmit and receive spectrum; the reported absence of the expected pressure peak near 4 MHz (the single-device M03 resonance) in the 5×5 polymer array's transmit spectrum is the motivating instance and illustration, while the required result is the general predictor over those parameters. (2) End-to-end SNR and penetration depth versus frequency: measure the noise floor and end-to-end signal-to-noise ratio of pulse-echo imaging — including front-end electronics and realistic coupling losses, with the front-end chain endpoints and the noise-floor definition stated explicitly — and quantify the maximum usable penetration depth as a systematic function of drive frequency across the array's usable bands, stating explicitly the criterion that defines 'usable' (the signal-to-noise-ratio or contrast threshold and the medium in which it is evaluated). (3) Frequency-dependent trade-offs and design rules: from (1) and (2), map the frequency-dependent trade-offs among transmit pressure, receive sensitivity, and axial/lateral resolution for the array geometries in question and derive explicit design rules (membrane diameter, pitch, electrode coverage, addressing scheme) for multi-frequency portable imaging.

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